b) The sum of the age of two sisters is 20 years. If one of them is 4 years younger than other, find their age.​

Answer:

x+y-200=0

Step-by-step explanation:

ax = x

by = y

c = 200 but we convert it to negative 200 after moving it from the RHS to LHS

So x+y=200 will be x+y-200=0 in the form ax + by + c =0

Answer:

D. X/3=1

Step-by-step explanation:

A. 8x = 28

8(3) = 28

24 = 28

Option A is wrong

B. x - 19 = 16

3 - 19 = 16

-16 = 16

Option B is wrong

C. 28 + 3 = 25

31 = 25

Option C is wrong

D. X/3=1

3/3 = 1

1 = 1

Option D is correct.

The sequence generated recursively by the rule is 1, 0.5, 0, -5, -2.5, 2, 7.25, ...

A recursive rule is a mathematical rule that describes how to calculate the value of a term in a sequence or function based on the values of previous terms. In other words, a recursive rule defines a sequence or function in terms of itself.

To apply a recursive rule, we start with one or more initial terms and then use the rule to generate the subsequent terms. The rule involves a formula that expresses each term in the sequence or function as a function of the previous terms. This process continues indefinitely, generating an infinite sequence or function.

Recursive rules are often used in mathematics to define sequences and functions that have a recursive structure, such as the Fibonacci sequence or the factorial function. They can also be used to define algorithms for solving problems in computer science and other areas.

One advantage of recursive rules is that they can provide a concise and elegant way of defining complex sequences or functions. However, they can sometimes be difficult to work with, as they can lead to complicated and recursive formulas that are hard to evaluate or simplify.

To generate the sequence 1, 0.5, 0, -5, ... recursively, we can use the following rule:

a_n = (a_{n-1} - 3a_{n-2})/2

where a_n represents the nth term in the sequence.

Using this rule, we can generate the sequence as follows:

a_1 = 1 (given)

a_2 = 0.5 (given)

To find the next term, we use the recursive rule:

a_3 = (a_2 - 3a_1)/2 = (0.5 - 3(1))/2 = -1

Continuing in the same way, we can find the next terms:

a_4 = (a_3 - 3a_2)/2 = (-1 - 3(0.5))/2 = -2.5

a_5 = (a_4 - 3a_3)/2 = (-2.5 - 3(-1))/2 = 2

and so on. Thus, the sequence generated recursively by the rule is 1, 0.5, 0, -5, -2.5, 2, 7.25, ...

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The correct option is (d) if A is divided by 2, B is divided by approximately 1.414.

Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
If A varies inversely as the square of B, it means that A is equal to some constant k divided by the square of B:

A = k/B²

To find the effect on B when A is multiplied by 4, we can use the inverse variation formula and substitute 4A for A,

4A = k/B^2

Simplifying this expression, we get:

B² = k/(4A)

To find the effect on B when A is multiplied by a certain factor, we can use this formula and substitute the new value of A,

a) If A is multiplied by 1.5:

1.5A = k/B²

B² = k/(1.5A)

The effect on B depends on the value of k and the original value of B, which are not given. So we cannot determine the effect on B with the information given.

b) If A is multiplied by 4:

4A = k/B²

B² = k/(4A)

Since 4A is four times the original value of A, B^2 will be divided by 4, so B will be multiplied by √4, which is 2. Therefore, when A is multiplied by 4, B is multiplied by 2.

c) If A is multiplied by 2:

2A = k/B²

B^2 = k/(2A)

Since 2A is half the original value of A, B^2 will be multiplied by 2, so B will be divided by √2, which is approximately 1.414. Therefore, when A is multiplied by 2, B is divided by approximately 1.414.

d) If A is divided by 2:

A/2 = k/B²

B² = k/(A/2)

Since A/2 is half the original value of A, B² will be multiplied by 2, so B will be divided by √2, which is approximately 1.414. Therefore, when A is divided by 2, B is divided by approximately 1.414.

Therefore, the correct option is (d) if A is divided by 2, B is divided by approximately 1.414.

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The inverse of the given function could be; y = √x / 7 + 8

Suppose that the given function is [tex]f:X\rightarrow Y[/tex]

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

[tex]f^{-1}: Y \rightarrow X[/tex]

This simply means, inverse of 'f' is undo operator, that takes back the effect of 'f'

We have been given the function as g(x)=7(x-8)² +3 for 8 ≤ x < ∝

Function that can reverse into another function is known as an inverse function or anti function to find y when x is swapped with another variable, we must first determine the inverse function.

On the other hand, the inverse function and the original function have interchangeable domains and ranges.

y = 7(x-8)²

(x-8)² = y/7

x - 8 = y / 7

x = √y / 7 + 8

Or

y = √x / 7 + 8

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Answer:

The number line with the added values would look as follows:

< -40/8 -5 ⟳ √3 -4 5/8 -3 √16 -2 7/12 -1 0 1 2 3 ^3√27 4 5 >

According to the standard conversion rates 1.78 is equal to 5.696 feet.

We measure the distance between any two bodies in the terms of meter but when the distance is a small one, we can also use the unit called foot and these two units are interconvertible.

According to the standard us conversion rates one meter is equal to 3.2 ft.

We can use this same conversion rate to find the measurement of 1.78 m into ft.

So, we will write,

1 m = 3.2ft

1.78m = 1.78 x 3.2 ft

1.78m = 5.696 ft.

So, we have found that 1.78 m is equal to 5.696 feet.

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Therefore, the expression that equals 3B - 3C in standard form is -21x² - 6x + 24.

In mathematics, an expression is a combination of numbers, variables, and operations that can be evaluated or simplified to obtain a single value or another expression. In algebra, expressions are often used to represent mathematical relationships or formulas, and can be manipulated using various algebraic techniques such as factoring, expanding, simplifying, and solving for unknown variables. Expressions are also used in calculus, probability theory, and many other branches of mathematics to describe mathematical models and relationships.

Here,

We can start by substituting the expressions for B and C into the expression for 3B - 3C and simplifying:

3B - 3C = 3(-3x - 7x²) - 3(-x² - 8 - x)

= -9x - 21x² + 3x² + 24 + 3x

= -21x² - 6x + 24

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The required length for line segment K'N' is 9 units. So correct option is C.

A trapezoid is a two-dimensional geometric shape that is defined as a quadrilateral with one pair of parallel sides. It is also known as a trapezium in some countries. The other two sides of a trapezoid are typically non-parallel and can be of different lengths.

Trapezoids can be classified into two types: isosceles trapezoids and non-isosceles trapezoids. Isosceles trapezoids have equal lengths of the non-parallel sides, while non-isosceles trapezoids have unequal lengths.

The area of a trapezoid can be calculated using the formula: (base1 + base2) x height / 2, where base1 and base2 are the lengths of the parallel sides, and height is the perpendicular distance between the parallel sides.

The perimeter of a trapezoid can be calculated by adding the lengths of all four sides together. If the trapezoid is isosceles, the perimeter can be calculated using the formula: 2 x (side length) + (sum of the lengths of the parallel sides).

Trapezoids can also be used to solve problems in real-world situations, such as calculating the area of a trapezoidal roof or finding the distance between two parallel lines. They are also commonly used in geometry problems and proofs.

In summary, a trapezoid is a quadrilateral with one pair of parallel sides. It can be classified as isosceles or non-isosceles and can be used to calculate area and perimeter, as well as solve problems in geometry and real-world situations.

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The solution is, the value is 17.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

here, we have,

from the diagram we get,

it is a right angled triangle.

now, we know, by Pythagorean theorem ,

15^2+ 8^2

=225+ 64

=289

=17^2

Hence, The solution is, the value is 17.

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Diane's monthly payment for borrowing $3,000 at 13.5% APR over 36 months is $101.81.

We can use an online finance calculator to compute the monthly payment, setting the following parameters.

The monthly payment shows the periodic payment that must be made to settle the loan with the finance charges.

N (# of periods) = 36 months

I/Y (Interest per year) = 13.5%

PV (Present Value) = $3,000

FV (Future Value) = $0

Results:

Monthly payments (PMT) = $-101.81

Sum of all periodic payments = $-3,665.01

Total Interest = $665.01

Thus, Diane will pay $101.81 monthly for 36 months.

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Answer: The value of sinB is b/c

Step-by-step explanation:since sinB =P/H

Here, P=perpendicular

         H=hypotenuse

so here, P=b and H=c

sinB=b/c

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The slope of each line on the given graph is:

Figure 1: -1/4

Figure 2: 0

Figure 3: -4

Figure 4: 4

The slope (m) of a linear relationship is calculated as rise/run = change in y / change in x.

Figure 1:

Slope (m) = change in y / change in x = -1/4 (the line declines, so the slope will be negative).

Figure 2:

Slope (m) = 0 (this is because there is no rise but run), thus, the slope of any horizontal line is always 0.)

Figure 3:

Slope (m) = change in y / change in x = -4/1 = -4 (the line declines, so the slope will be negative).

Figure 4:

Slope (m) = change in y / change in x = 4/1 = 4 (the line rises, so the slope will be positive).

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The equation √(x - 1) - 5 = x - 8 has two solutions 2 and 5. The valid solution is 5.

The set of values that can be satisfies the given condition in the equation is known as the solution.  We can solve the equation by adding or subtracting the same integer from both sides. Here adding or subtracting doesn't change the value of the equation.

Here we have

√(x - 1) - 5 = x - 8  

Solve the above equation to get the solutions

√(x - 1) - 5 = x - 8    

Add 5 on both sides

√(x - 1) - 5 + 5 = x - 8 + 5

√(x - 1)  = x - 3  

Do squaring on both sides

[√(x - 1) ]² = (x - 3)²    

[ x - 1 ] = (x² + 9 - 6x)    

x² + 9 - 6x - x + 1 = 0

x² - 7x + 10 = 0  

Now factorize the above equation

x² - 5x - 2x + 10 = 0      

x(x - 5) - 2(x - 5) = 0

(x - 5) (x - 2) = 0

(x - 5) = 0     and     (x - 2) = 0

x = 5                       x = 2      

at x = 2 => √(2 - 1) - 5 = 2 - 8    

=> √1 - 5 = 2 - 8    

=>   - 4 = -6 [ which is not true ]

at x = 5 => √(5 - 1) - 5 = 5 - 8      

=> √(4 - 1) - 5 = - 3  

=> 2 - 5 = -3  [ which is true ]

Therefore,

The equation √(x - 1) - 5 = x - 8 has two solutions 2 and 5. The valid solution is 5.

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Answer:

Step-by-step explanation:

Answer:

x=8

Step-by-step explanation:

calculate

We can expect 40 defective parts in a shipment of 1,000 parts.

We can use proportions to solve this problem.

The proportion of defective parts in the first shipment is:

16/400 = 0.04

This means that 4% of the parts in the first shipment are defective.

We can use this proportion to estimate the number of defective parts in a shipment of 1,000 parts.

If 4% of the parts are defective, we can set up the following proportion:

4/100 = x/1000

where x is the number of defective parts in the shipment of 1,000.

Simplifying the proportion, we get:

0.04 = x/1000

To solve for x, we can multiply both sides by 1000:

0.04 * 1000 = x

x = 40

Therefore, we can expect 40 defective parts in a shipment of 1,000 parts.

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The slope of the line passing through the points (2, 8) and (2, -4) is undefined.

The slope of the line passing through the points (-7, 8) and (2, 8) is zero.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope, m = (-4 - 8)/(2 - 2)

Slope, m = (-12)/0

Slope, m = undefined.

Since the change in the y-axis equals to zero, the slope of this line is equal to zero:

Slope, m = (8 - 8)/(2 - (-7))

Slope, m = 0/9

Slope, m = 0

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When t = 4, the expression 3⋅2ᵗ evaluates to 48.

Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the given expression, all of which are separated by the arithmetic sign +.

An expression consists of one or more numbers or variables along with one more operation.

When t=4, the expression 3⋅2ᵗ evaluates to:

3⋅2⁴ = 3⋅16 = 48

Hence, when t = 4, the expression 3⋅2ᵗ evaluates to 48.

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54 centimetres, rounded to two decimal places, is comparable to around 21.26 inches.

The Imperial and US Customary measuring systems both utilise the inch as their unit of measurement.

It is the unit of length.

Furthermore, length is measured in centimetres,

Used in the International System of Units,

This is the metric system's present configuration.

There are 21.26 inches in 54 cm (centimeters).

To convert centimeters to inches,

You can use the following conversion:

1 inch = 2.54 cm

Therefore,

To convert 54 cm to inches,

You can divide 54 by 2.54:

54 cm / 2.54 = 21.26 inches

So 54 cm is equivalent to approximately 21.26 inches,

Rounded to two decimal places.

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The conversion of 23/32 cm in inches is 0.283464844 inches.

Centimeter (cm) and inch are both units of measurement used to express length or distance.

Centimeter is a metric unit of length used in the International System of Units (SI) and is equal to one hundredth of a meter.

To convert 23/32 centimeters (cm) to inches, we can use the conversion factor of 1 cm = 0.393701 inches.

First, we can convert 23/32 cm to cm as a decimal by dividing the numerator (23) by the denominator (32):

23/32 cm = 0.71875 cm

Then, we can use the conversion factor to convert 0.71875 cm to inches:

0.71875 cm × 0.393701 inches/cm = 0.28346484375 inches (rounded to nine decimal places)

Therefore, 23/32 cm is approximately equal to 0.283464844 inches.

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Correct Question:

What is the conversion of 23/32 cm in inches ?

None of the given equations gives the correct answer, the answer is none of the options.

The equation from the calculation is:

y = 375(0.9834)ˣ

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal and joined by the equals sign "=". Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

The data gives the relation between time and temperature.

We are asked to find the time and temperature relation as an equation.

We are given five equations as options.

a) T(x) = 375(0.5)ˣ

x is time and T is temperature.

Now we will give the value of x = 10 in this equation.

T(10) = 375 * 0.5¹⁰ = 0.366

This is not the value given in the table.

So this is not the equation.

b) T(x) = -50x + 375

  T(10) = -50 * 10 + 375 = -500 + 375 = -125

This is not the equation.

c) T(x) = -25x² + 375

   T(10) = -25 * 10 * 1 0 + 375 = -2500 +375 = -2125

This is not the equation.

d) T(x) = 50x - 375

   T(10) = 50 * 10 - 375 = 500 - 375 = 125

This is not the equation.

e) T(x) = 25x² -75x + 375

  T(10) = 25 * 10 * 1 0 -75 * 10 + 375 = 2500 -750 +375 = 2125

The general form of the exponential equation is:

y = abˣ

375 = ab⁰= a

325 = ab¹⁰

275 = ab²⁰

275/325 = b¹⁰

b = 0.9834

So the equation for this data is:

y = 375(0.9834)ˣ

Since none of the given equations gives the correct answer, the answer is none of the options.

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Answer:

86.1825503

Step-by-step explanation

190 pounds to kg is 86.1825503

Answer:

4.5%

Step-by-step explanation:

The total percentage decrease in the investor's stock account was 4.5%. This is calculated by taking the decrease in Company A (3%) and Company B (6%) and adding them together to get a total decrease of 9%. This percentage is then divided by two (since there are two companies) to get 4.5%.

Answer:

1 = 37° 2= 53° 3=106° 4=74°

Step-by-step explanation:

I apologize in advance since I am not the best at explaining but I'll do my best:

All triangles add up to 180° since you already know 106° you can subtract 106° from 180° to get 74° so you divide that by 2 to get angle 1 since both angles will be the same (since all the triangles are isosceles triangles) now since it's a rectangle all angles add up to 90° so subtract 37° from 90° to get angle 2 now you only have 3 and 4 left 3 is 106° since it's the same as the first triangle now to find four since you know angle 2 you know both of the bottom angles are 53° now 53 times 2 equals 106° so you subtract 106° from 180° and get 74°

Answer:

122.5 feet

Step-by-step explanation:

[tex]\frac{4}{35}[/tex] = [tex]\frac{14}{x}[/tex]  cross multiply and solve for x

4x = 490  Divide both sides by 4

x = 122.5

The length of B'C' is 15k.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

ABCD is the original image and A'B'C'D' is the dilated image.

BC is having length of fifteen units.

We need to find B'C'

Let k be the scale factor.

A dilation is a transformation which preserves the shape and orientation of the figure, but changes its size.

B'C'=kBC

B'C'=15K

Hence, the length of B'C' is 15k.

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The solution for n of the expression in this problem is given as follows:

n = 5.

With the application of the distributive property, the outer term multiplies each of the inner terms of the expression. If possible, these inner terms than can be added or subtracted combining the like terms.

The mistake in the solution was applying the distributive property to 3(2n - 7), as 3 has to multiply both terms, 2n and -7, hence:

3(2n - 7) = 6n - 21.

Thus the solution to the expression is obtained as follows:

6n - 21 = 9

6n = 30

n = 30/6

n = 5.

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Answer:

-2+sqrt(2)i and -2-sqrt(2)i

Step-by-step explanation:

use system of equations

xy = 6

x+y=-4

(-4-y)y=6

-y^2 -4y + 6 = 0

Use quadratic formula

y = -2 ± sqrt(2)i

Now substitute

x + (-2 ± sqrt(2)i) = -4

X = -4-(-2±sqrt(2)i) = -2±sqrt(2)i

are you sure you typed the question right?